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Improving “National Brands”: Reputation for Quality and Export PromotionStrategies
Julia Cage, Dorothee Rouzet
PII: S0022-1996(14)00158-5DOI: doi: 10.1016/j.jinteco.2014.12.013Reference: INEC 2830
To appear in: Journal of International Economics
Received date: 25 January 2013Revised date: 29 November 2014Accepted date: 21 December 2014
Please cite this article as: Cage, Julia, Rouzet, Dorothee, Improving “National Brands”:Reputation for Quality and Export Promotion Strategies, Journal of International Eco-nomics (2015), doi: 10.1016/j.jinteco.2014.12.013
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Improving “National Brands”: Reputation for Quality
and Export Promotion Strategies
Julia Cagea, Dorothee Rouzetb,∗
aHarvard UniversitybOECD
Abstract
This paper studies the effect of firm and country reputation on exportswhen buyers cannot observe quality prior to purchase. Firm-level demandis determined by expected quality, which is driven by the dynamics of con-sumer learning through experience and the country of origin’s reputationfor quality. We show that asymmetric information can result in multiplesteady-state equilibria with endogenous reputation. We identify two typesof steady states: a high-quality equilibrium (HQE) and a low-quality equi-librium (LQE). In a LQE, only the lowest-quality and the highest-qualityfirms are active; a range of relatively high-quality firms are permanently keptout of the market by the informational friction. Countries with bad qual-ity reputation can therefore be locked into exporting low-quality, low-costgoods. Our model delivers novel insights about the dynamic impact of tradepolicies. First, an export subsidy increases the steady-state average qualityof exports and welfare in a LQE, but decreases both quality and welfarein a HQE. Second, there is a tax/subsidy scheme based on the duration ofexport experience that replicates the perfect information outcome. Third, aminimum quality standard can help an economy initially in a LQE movingto a HQE.Keywords: product quality, product differentiation, export promotion, in-dustrial policy, trade, asymmetric informationJEL: F12, F13, L15, L52, O14, O24
∗Corresponding authorEmail addresses: [email protected] (Julia Cage), [email protected]
(Dorothee Rouzet)
Preprint submitted to Journal of International Economics November 29, 2014
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1. Introduction
Why do country-of-origin labels matter to consumers? This question findsno clear answer in standard models of international trade, which assumethat consumers are perfectly informed about the characteristics of everyavailable product and leave no role for country reputations. However, as alarge literature on experience goods has shown, quality is not fully known toconsumers prior to purchase for a wide range of goods. Inferring the qualityof a good requires time and is achieved both through search and throughexperience. For these categories of goods, country-of-origin affects productevaluations and consumers’ decisions.1
In this paper, we argue that a “national brand image” matters becauseit provides an anchor for the expected unobservable quality of imports suchthat a bad country reputation can become self-fulfilling. Consumption de-cisions, in practice, are based on a limited information set available to con-sumers at the time of purchase: information gathered as a result of pastconsumption experience and word-of-mouth diffusion, but also the countrywhere the good was manufactured. For new and unknown foreign goods, themain piece of information available to consumers besides observable charac-teristics is the “made in” label, which indicates the country of manufacturingand creates a key role for national reputations. We call “national reputa-tion” the common component of consumers’ expectations of the quality ofgoods produced within a given country. Country reputations determine thequality that buyers expect before they learn any information specific to aproduct. We show how the dynamics of consumer learning and countryreputation can create multiple equilibria with self-fulfilling expectations.
More specifically, we consider an infinite-horizon two-country model witha continuum of potential foreign exporters heterogeneous in quality, and aconstant flow of new potential exporters per period. Each new firm drawsa quality parameter from a fixed distribution of firm technologies and hasthe option to produce a good of this quality. The decision to produce isendogenous: potential foreign exporters decide whether to enter the marketand when to exit, taking into account the impact of their decisions on ex-pected future sales. We assume that the cost of producing one physical unit
1Schott (2008) documents that the prices that US consumers are willing to pay forChinese exports are substantially lower than the prices they are willing to pay for OECDexports of the same products. Many survey-based studies in the marketing literature,summarized by Roth and Diamantopoulos (2009) also emphasize the role of country-of-origin labels in setting consumer perceptions of quality.
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of the good is monotonically increasing in quality, but the cost per quality-adjusted unit is decreasing in quality. Quality is known to firms but notobserved by consumers before purchase. Hence, import demand dependson perceived quality, which has two components. Goods imported from agiven country are first evaluated according to a country-wide prior, whichis endogenously determined by the average quality of the country’s exportsin a long-run industry equilibrium. Importers then learn about the truequality of firms that have exported in the past. The fraction of informedconsumers increases with the time a firm has been active on the market. Theeffect of the country prior will thus prevail for new exporters and fade overtime as buyers gain familiarity with individual foreign brands. As a con-sequence, asymmetric information fosters entry by low-quality firms, whichearn higher profits than under perfect information by free-riding on high-quality expectations. It depresses profits of the highest-quality firms, forcedto incur initial losses in order to reveal information about their type.
We characterize the equilibrium structure. There are two types of steadystates with endogenous reputation: a high-quality, high-reputation equi-librium (HQE), and a low-quality, low-reputation equilibrium (LQE). Ina LQE, only the lowest-quality and the highest-quality firms are active; arange of relatively high-quality firms are permanently kept out of the marketby the informational friction. Fly-by-night firms export only for one periodin this equilibrium; on the contrary, in a HQE, low-quality firms that enterintially as fly-by-nights can last longer than one period. We show that therecan be multiple equilibria, such that countries with bad quality reputationcan be locked into exporting low-quality, low-cost goods. Where multipleequilibria exist, reputation shocks can then have self-fulfilling effects.
This last result challenges the effectiveness of some export-led growthstrategies which rely on exporting low-quality, low-cost goods and graduallymoving up to higher quality, higher unit-value goods. A number of EastAsian economies have pursued such strategies in the past. Without policyintervention, we show that it may not be a feasible path if the economy istrapped in a self-fulfilling equilibrium in which the country’s reputation forlow quality prevents some high-quality firms from entering export markets.We therefore consider various policies that can be implemented in a low-quality equilibrium to promote exports and improve a country’s reputationabroad.
Our model delivers novel insights about the impact of the following tradepolicies. First, an export subsidy increases the steady-state average qualityof exports and welfare of the exporting country in a LQE, but decreasesboth quality and welfare in a HQE. This policy raises the incentives to
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export for all firms, but in a LQE it has a larger effect on high-quality firmswhich have a longer effective horizon. Conversely, in a HQE, it only leads toadditional entry by low-quality firms, which creates a negative reputationexternality on all exporters. Second, there is a tax and subsidy scheme basedon the duration of export experience that replicates the perfect informationoutcome. Finally, a minimum quality standard can help an economy initiallyin a LQE move to a HQE.
The remainder of this paper proceeds as follows. Section 2 reviews theliterature relevant to the present study. Section 3 lays out our modellingframework. Section 4 analyzes high-quality and low-quality steady-stateequilibria with endogenous reputation. Section 5 explores the effects ofdifferent policy instruments on quality, reputation and welfare. Section 6concludes.
2. Related Literature
This paper relates to the international trade and industrial organizationliterature on vertical quality differentiation and asymmetric information.This section briefly explains how our dynamic approach with a continuumof quality types and self-fulfilling reputations differs from the existing modelsof asymmetric information in exports.
Informational barriers to entry in international trade have been studiedby Mayer (1984), Grossman and Horn (1988), Bagwell and Staiger (1989),Bagwell (1991), Chen (1991), Dasgupta and Mondria (2012, 2013) andChisik (2003). Mayer (1984) was the first to investigate export subsidiesin the presence of initially uninformed consumers but did so without model-ing explicitly the process of consumer learning and expectations formation,and relied on pessimistic consumer beliefs. Dasgupta and Mondria (2013)develop a two-period model with similar features to ours, where the qualityof new exporters is unobservable and that of continuing exporters is knownby a fraction of consumers. They, however, focus on the role of interme-diaries in providing quality assurance and do not analyze the formation ofcountry reputations.
The articles that are the most closely related to the present paper areBagwell and Staiger (1989) and Chisik (2003) who both explore the inter-play between country reputation, exporting firm quality and optimal tradepolicy. While our paper builds on these pioneering works, it departs fromthem both in the assumptions and in the policy implications. In our model,exporting firms cannot signal their quality, so that information acquisition
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is entirely driven by the dynamics of consumer learning through experienceand the evolution of country reputations. We also introduce a richer qual-ity structure with a continuum of quality types rather than only two types;and a richer time structure with an infinite horizon model, while Bagwelland Staiger (1989) use a two-period model and Chisik (2003) considers astatic game. We are then able to model the process of reputation formationand investigate the transition dynamics of quality and reputation betweensteady states, between an uninformed prior and the steady state, or followingshocks.
In contrast to the existing literature, we obtain two distinct regimes(HQE and LQE). In the LQE regime, non-exporters are in the middle of thequality distribution, while the lowest-quality firms and the highest-qualityfirms are not precluded from entering the market. While Grossman (1990)has anticipated the hollowing out of the middle of the quality distribution,our paper is the first to formalize these results.2
Note moreover that our paper is one of the very few that focus oncountry-of-origin reputations rather than on pure informational barriers toentry. Together with Chisik (2003) and Dasgupta and Mondria (2012) weare the first to model self-fulfilling country reputations – and we improveon these previous works by introducing a dynamic model with a more full-fledged quality dimension. Country-of-origin reputations are certainly re-lated to the topic of exporters of an unknown quality, but also encompassa different set of issues. In particular, their policy implications can departfrom those of informational asymmetries as a policy goal is to push the econ-omy on a path to a different, higher welfare equilibrium. In that respect,our modeling of country-of-origin reputations is related in spirit to the ap-proach of the statistical discrimination literature, though policy instrumentsnaturally differ from those considered in a labor market framework (for asurvey of the literature on discrimination in the labor market, see Lang andLehmann, 2012).
Furthermore, our model delivers novel insights about the impact of tradepolicies. It is well-understood in the literature that export subsidies can bewelfare-improving or -decreasing depending on whether information exter-nalities lead to a problem of insufficient or excessive entry, respectively.Bagwell and Staiger (1989) focus on the welfare-improving case: they ex-plore a situation in which asymmetric information yields socially insufficient
2In Bagwell and Staiger (1989) and in Chisik (2003), there are only two types of firms,so by construction there cannot be the hollowing out of the middle that we obtain.
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entry. A subsidy can induce high-quality firms to enter the export market,whereas absent the subsidy their entry may be blocked by their inability tosell at prices reflecting their true quality. In contrast, Grossman and Horn(1988) point out that asymmetric information may lead to socially exces-sive entry when the quality choice is endogenous. In their model, an exportsubsidy does encourage entry but the marginal entrants are those with thegreatest incentive to produce low-quality goods, reducing average quality(see Grossman, 1990). Our model encompasses both effects. We obtain apositive effect of an export subsidy in the LQE case: the subsidy inducesfirms in the middle of the quality distribution to export, and the overall ef-fect on average quality is positive.3 In a HQE, however, the dominant effectof a subsidy is to worsen the socially excessive entry of low-quality firms.We also depart from Chisik (2003) where export subsidies are of no use sincethey do not alter the relative payoffs of high-quality and low-quality firms.In our model, high-quality firms face a longer effective time horizon, so thateven a subsidy granted indiscriminately to all exporters tilts the incentiveto export in favor of high-quality firms.
Next, we analyze the effect of other trade policies, some of which havebeen overlooked in the literature. We show that if the government can ob-serve how many periods a firm has been in the market, it can design atax and subsidy program that similarly changes the relative incentives ofhigh-quality and low-quality firms and improves both quality and reputa-tion. This result extends the finding by Bagwell and Staiger (1989) thatan introductory phase tax on exporters followed by a mature phase subsidyimproves welfare. The first-period tax can be interpreted as an export li-cense. Chisik (2003) explores the effect of a similar policy – an optionaltax that is rebated only to firms that produce high quality – but imposesmore stringent information requirements by assuming that the governmentperfectly learns the quality of every firm’s product after the initial period.Alternatively, we show that a minimum quality standard can help move toa more favorable equilibrium.
Our paper also relates to the industrial organization literature dealing
3This would still be the case if we allowed for an endogenous quality choice, althoughfly-by-night firms would then always choose the minimum quality level.
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with experience goods4 as well as with labels and quality certification.5
Lastly, the formation of collective reputations had been modelled by Ti-role (1996) in a moral hazard setting, where group reputation is both theoutcome and a determinant of individual behavior.6
3. Model Set-Up
We develop a model with two countries. We focus on the industry equi-librium in an export-oriented sector in the home country, for which theforeign country is the importer. In the home country, there is a continuumof potential exporters j of mass 1 being born every period. In the foreigncountry, there is a pool of importers indexed by i, each of whom demandsone unit of the good. All firms in the industry produce for export only.7
3.1. Firms
Each new potential exporter j draws a quality parameter θ from a Paretodistribution G (θ) with support on [θm,∞) and shape parameter α > 1. Wedenote the unconditional expectation of quality draws by µ0, equal to
αα−1θm.
Each firm j has the option to produce one unit of a good of quality levelθ (j).8
4Several early papers (Shapiro, 1983; Riordan, 1986; Farrell, 1986; Liebeskind andRumelt, 1989) have studied entry and pricing strategies for experience goods in a closedeconomy framework. Bergemann and Valimaki (1996, 2006) incorporate the experimenta-tion and learning processes by consumers. We develop these insights further by consideringthe demand for imports, where initial priors depend on country-of-origin, and reputationsare built not only for specific firms but also for exporting countries as a whole.
5A strand of it assuming that quality is unknown to consumers (see e.g. Perrot andLinnemer, 2000). This literature focuses on the signaling role of labels: labels act asquality signals for individual firms which seek to signal quality and build consumer trust(see e.g. Grossman, 1981; Klein and Leffler, 1981; Milgrom and Roberts, 1986; Lizzeri,1999), but there are no reputation externalities between firms.
6His model generates a high- and a low-reputation steady-state equilibrium, but forgiven initial conditions, there is a unique equilibrium. An interesting result is that aone-time shock can have permanent effects on collective reputation, as in our model.
7Or, equivalently, markets are segmented. We could easily extend the model to allowfirms to serve their domestic market as long as the decisions to enter the domestic andexport markets are separable. The key assumption is that there is no information flowingbetween buyers located in different geographic markets.
8For simplicity we do not model the quality choice. We can think of the exogenousquality draw as determined on the domestic market before considering the decision toexport, or as a technology blueprint which comes from an R&D process with uncertainoutcome.
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At the beginning of every period, firms decide whether to stay active andexport, or shut down. If it produces and sells, firm j incurs a cost wθ (j)+k,including both production and transport costs (with k > 0 and 0 < w < 1).Hence, profits at period t+ s of an active firm j born at date t are:
πt+s (j) = pt+s (j)− wθ (j)− k (1)
where pt+s (j) is the price at which firm j sells its output.A firm can freely exit at any period and realize zero profits from this
period onwards. However if it chooses to exit the export market in a givenperiod, it cannot re-enter later.9 Moreover, each firm has a probability(1− δ) per period of suffering from an exogenous shock that forces it toexit, independent of both quality and the firm’s age. This exogenous “exitshock” acts as a discount rate, as in Melitz (2003).
3.2. Buyers
In the foreign country, each potential importer demands one unit of thegood. Potential demand for imported goods is assumed to be large, in thesense that the market size is sufficient for all home exporters to find a buyerat a price that does not exceed the expected value of their goods. Thetrue utility from consuming a good of quality level θ (j) is θ (j) but is notobservable before purchase.10
At the beginning of every period, each active firm j is randomly matchedto a foreign buyer i. The firm cannot sell to another importer in that period,nor can the buyer purchase from another exporter before the next period.The firm then sets the price equal to the expected value of the good for itsbuyer.11 As θ (j) is not observed, the maximum price that an importer i iswilling to pay for the output of firm j at time t+ s is given by its expectedquality from the perspective of the buyer.
9This assumption is inconsequential for the steady-state analysis. It rules out coordi-nation problems among high-quality firms along the transition path.
10The indirect utility buyer i receives from the good sold by firm j at time t + s isuit+s (j) = θ (j)− pt+s (j), which can be derived from an additively separable utility func-
tion where buyer i consumes a numeraire good and one unit of the imported differentiatedgood.
11We assume that firms hold all the bargaining power and receive the full expectedsurplus of the transaction. Long-term contracts between exporters and importers are ruledout in this setting: all contracts are one-period sales contracts and firms are matched tocustomers for one period only. In particular, there cannot be price schedules resembling anintroductory pricing strategy, whereby buyers would pay a low price in the initial periodand offer a sequence of prices contingent on their future consumption experience.
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• • • • • •
Each activefirm is matchedwith a buyerand observeswhether thebuyeris informed.
The price isset by the firm,and productionand salestake place.
For each goodthat was sold,the fraction ofinformed buyersrises from ρ (s)to ρ (s + 1).
With probability(1 − δ),each firm isforced to exitby a shock.
Firms thatsurvivedecide whetherto stay active.
New firmsare born(cohort t + s).
Figure 1: Timing of actions
There are two types of buyers, informed and uninformed. Uninformedbuyers have no information specific to firm j. The only information attheir disposal is the “national reputation”, i.e. a prior µt+s about expectedquality among all foreign exporters. µt+s is common across buyers and isendogenized in Section 4. Informed buyers know the true quality of firmj, either because they have past experience from consumption of good jor because they have received information from another importer who has.The price received by firm j matched with buyer i in period t+s is thereforeµt+s if i is uninformed, and θ (j) if i is informed.
In the first period when a firm j enters the market, all importers areuninformed about j. Then, if firm j has exported s times in the past, afraction ρ (s) of buyers are informed, where we make the natural assump-tion that the fraction of informed buyers increases as the firm gains exportexperience (see Appendix B for a formal microfoundation).
Assumption 1. ρ′ ≥ 0, ρ (0) = 0, and lims→∞
ρ (s) = 1.
For expositional simplicity we drop the j notation in the next sectionsand refer to “firm θ” instead of “firm j with quality parameter θ”.
3.3. Timing
For a given cohort of firms born at date t, each new firm draws a param-eter θ and decides whether to export or not at t. For each s ≥ 1, at timet+ s, the timing is shown in Figure 1.
3.4. Perfect Information
Under perfect information, all θ are observable by all parties. All firmsreceive a price p∗t+s equal to true quality regardless of how long they havebeen exporting: p∗t+s (θ) = θ for all s.
Therefore, it follows from (1) that firms are active exporters if and onlyif θ ≥ θ∗, where the perfect information threshold is defined as:
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θ∗ ≡k
1− w(2)
The perfect information threshold is key for our analysis as we will showthat under asymmetric information, per-period profits converge over timetowards their perfect information value. Moreover, from a global welfarepoint of view, it is not optimal for firms with quality below θ∗ to enterexport markets – in this case, the value of the output to consumers is lowerthan the opportunity cost of production. However, given that exporters donot internalize the impact of their decisions on consumer surplus, it canbe profitable for firms with quality below θ∗ to enter temporarily underasymmetric information.
3.5. Imperfect Information: Price and Profits
Under asymmetric information, suppose µt is the buyers’ prior about theexpected quality of foreign goods at time t (“national reputation”), taken asexogenous by individual firms although it is endogenous at the country level.We derive its equilibrium value in Section 4. The price offered to a firm bornat date t is either the country-wide prior if the buyer is uninformed, or itstrue quality if the buyer is informed. In the first period in which a firm isactive, no buyer has any information specific to the firm, so that the priceonly depends on the prior: pt+1 = µt+1. Then in the following periods,conditional on the firm still being active, the price is set according to thefollowing rule:
pt+s =
{
θ with probability ρ (s− 1)µt+s with probability 1− ρ (s− 1)
for s ≥ 1 (3)
where ρ (s− 1) is the fraction of informed buyers for a firm that has pre-viously exported (s− 1) times. The expectation of the price converges tothe perfect information price θ over time if the firm stays in the marketindefinitely.
The expected profits of the firm in future periods, conditional on remain-ing active, are the difference between its expected price and its productioncost:
Etπt+s = [ρ (s− 1)− w] θ + [1− ρ (s− 1)]Etµt+s − k (4)
Expected profits place a larger weight on true quality and a smallerweight on national reputation as the firm gains tenure into exporting. Itimmediately follows that if reputation is time-invariant, which will be thecase in a steady-state equilibrium, a firm with quality above the country
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prior (θ > µ) expects to realize an increasing sequence of profits over time,while a firm with quality below the country prior (θ < µ) expects decreasingprofits. For all active firms, if µ is constant, the price is monotonicallyconverging towards θ and per-period profits are monotonically convergingtowards their perfect information value (1− w) θ − k.12
To ensure that expected profits from repeat purchases are increasing intrue quality, we assume that the updating parameter is large enough relativeto the cost of producing quality:
Assumption 2. ρ (1) > w
Firms are free to exit at any date. In each period t, a firm of qualityθ having exported s times in the past stays active if the expected presentvalue of doing so, PVt (θ, s), is positive:
PVt (θ, s) =
T (θ)∑
u=0
δu(
[ρ (s+ u)− w] θ + [1− ρ (s+ u)]Etµt+u − k)
(5)
where Etµt+u = µt+u for all u since there is no aggregate uncertainty, andT (θ) is the exit date (possibly infinity) that maximizes the firm’s intertem-poral problem.
4. Industry Equilibrium
4.1. Equilibrium Definition
We define a steady-state industry equilibrium as one in which nationalreputation is endogenously pinned down by the average quality of a country’sexports and the quality distribution is stationary. Country reputations aretaken as exogenous by individual firms. In each period t, let Mt (θ, s) be thenumber of active firms of quality θ having previously exported s times. LetNt (θ) =
∑ts=0Mt (θ, s) be the total number of active firms of quality θ. We
derive θt as the average quality of exports across quality levels and cohortsof firms:
θt =
∫
∞
θmθNt (θ) dθ
∫
∞
θmNt (θ) dθ
(6)
A new firm of quality θ is active at t+ 1 if its expected present value ofdoing so is positive. Hence the number of active new firms per quality level
12In Appendix C, we characterize the path of prices for a given cohort of firms.
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is:
Mt+1 (θ, 0) =
{
g (θ) if PVt+1 (θ, 0) > 00 if PVt+1 (θ, 0) ≤ 0
(7)
where g (θ) is the PDF of the quality distribution.Among incumbent firms of quality θ having exported s times, δMt (θ, s− 1)
survive from period t to period t+1. They remain active if PVt+1 (θ, s) > 0in equation (5). Thus the number of active old firms is, for s ≥ 1:
Mt+1 (θ, s) =
{
δMt (θ, s− 1) if PVt+1 (θ, s) > 00 if PVt+1 (θ, 0) ≤ 0
(8)
We can then define the industry steady-state as an equilibrium withconstant reputation and a constant distribution of quality.
Definition 1 (Steady-State Equilibrium).{
µ, {M (θ, s)}s,θ
}
is a steady-state equilibrium if and only if:
i. For all θ ∈ [θm,∞) and all s ≥ 0, if Mt (θ, s) = M (θ, s) and Etµt+u = µfor all u ≥ 0, then Mt+1 (θ, s) = M (θ, s) in (7) and (8);
ii. If Mt (θ, s) = M (θ, s) for all θ ∈ [θm,∞) and all s ≥ 0, then θt = µ in(6).
Condition (i) ensures that the number of firms in each quality-age seg-ment is constant in the steady state. Condition (ii) states that the averagequality resulting from an equilibrium distribution of active firms is equalto the equilibrium country reputation. It guarantees that µ is constant ina steady state. In other words, a steady state with national reputation µis a rational expectations equilibrium if the average quality of active ex-porters is equal to buyers’ quality expectation. The endogenous entry andexit decisions induced by µ justify the reputation ex post.13
13In the numerical examples, we assume that country reputations evolve according to theactual quality of exported goods in the previous period as follows: µt+1 = µt+η
(
θt − µt
)
,
where η < 1 and θt is the average quality of foreign firms’ exports at period t. Settingη < 1 captures the slow-moving aspect of reputations and only matters for equilibriumstability. This equation is a reduced form for consumers’ updating process, where theimplied simplifying assumption is that η – which captures the speed at which beliefs areupdated – is constant. We adopt this simple rule-of-thumb formulation for beliefs updatingrather than modeling explicitly the Bayesian updating process for the sake of simplicity.This hypothesis is not necessary for our main steady-state results and policy implications,and only ensures that equilibrium stability holds under general conditions.
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4.2. Equilibrium Steady-State Reputation
Let θ (µ) be the average quality of exports as a function of constant be-liefs µ. An equilibrium steady-state reputation is a time-invariant reputationµ such that θ (µ) = µ.
To compute the fixed point(s) of θ (µ), we proceed as follows. First, wecharacterize firms’ entry and exit decisions. Second, we compute Mt (θ, s),i.e. the number of active firms of quality θ having previously exported stimes, and thus the average quality of exports as a function of µ. We thenderive the existence conditions for each type of equilibrium.
4.2.1. Sorting of Firms into Non Exporters and Exporters
Steady-state equilibria as defined by Definition 1 fall into one of tworegimes: a “high-quality equilibrium” (HQE) or a “low-quality equilibrium”(LQE), depending on the position of the equilibrium country reputationrelative to the perfect information threshold.
Definition 2 (HQE & LQE).
A steady-state equilibrium{
µ, {M (θ, s)}s,θ
}
is a high-quality steady-state
equilibrium if µ > θ∗, and a low-quality steady-state equilibrium if µ < θ∗.
The two regimes have different entry and exit patterns, due to the impactof asymmetric information and the dynamics of consumer learning. Com-pared to the perfect information case, the unobservability of quality initiallyfosters entry by low-quality firms but depresses profits of the highest-qualityfirms. In a HQE, a firm with quality equal to the country’s reputation wouldbe viable in a perfect information setting. All firms receive high prices asthey enter the market, which encourages entry. Therefore, imperfect infor-mation does not hinder entry of high-quality firms into export markets butgenerates excess entry by low-quality firms. On the contrary, in a LQE, afirm with quality equal to the country’s reputation would never export in aperfect information setting. Some low-quality firms still profit by free-ridingon the country reputation, but a range of firms with above-average qualityare permanently kept out of the market by the informational friction. Inother words, there is a hollowing out of the middle of the quality distribu-tion. Proposition 1 establishes the sorting of firms into non exporters andexporters in a HQE and in a LQE.
Proposition 1 (Sorting of Firms into Exporting: Two Regimes).In a HQE:
1. All entrants are initially active;
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2. Firms with θ < θ∗ expect to exit after T (θ) periods where T is weaklyincreasing in θ;
3. Firms with θ > θ∗ stay in the market until hit by the exogenous shock.
In a LQE:
1. Firms with quality θ < θL enter the export market and exit after sellingfor one period, where θL ≡ µ−k
w < µ < θ∗;
2. Firms with quality θ > θH enter and stay in the market until hit by the
exogenous shock, where θH ≡k−µ(1−Aρ)
Aρ−w > θ∗ and Aρ ≡ (1− δ)∑
∞
s=0 δsρ (s) .
3. Firms with quality θL ≤ θ ≤ θH never enter the market.
Proof: see Appendix A.1.
Figure 2 shows the sorting of firms according to their quality parameterin each regime. In a HQE (upper figure 2a), all low-quality firms (belowθ∗) find it profitable to enter initially as fly-by-nights, as they have lowproduction costs and can therefore reap positive expected profits as long asa small enough number of buyers have information about their type. Thehigher the country reputation, the higher the price they receive in the firstperiod. However, they become less profitable as consumers gain informationabout their quality through consumption experience. Low-quality firms thusface a decreasing sequence of expected profits converging to a negative value;they will eventually see their expected present value of profits turn negativeand exit. The lowest-quality firms exit first, and θT is the highest qualitytype that exits after selling for T periods.14 For high-quality firms (aboveθ∗), it is always profitable to enter and keep exporting. Firms betweenθ∗ and µ have expected profits declining over time, but positive in everyperiod. Firms above µ have expected profits increasing over time. Thehighest quality firms incur losses in the initial period but recoup these lossesin later periods once enough buyers have received information about theirtype; their expected intertemporal profits are always positive.
In a LQE (bottom figure 2b), there is a range of low-quality firms (be-low θL) that gain from the information asymmetry and realize positive first-period profits. However they would make losses if they were to stay active in
14Firms below θ∗ exit after T (θ) periods, where T (θ) is the exit date that max-imizes the firm’s intertemporal profit (see equation (5)). We can derive θT =
max{
k−[1−ρ(T )]µρ(T )−w
, θm
}
for T ≥ 1 and limT→∞ θT = θ∗ (See Appendix A.1).
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(a) High-Quality Equilibrium
(b) Low-Quality Equilibrium
Figure 2: Sorting of firms by θ
the second period. These firms therefore exit immediately after selling once,while in a HQE low-quality firms that enter initially as fly-by-nights canlast longer than one period. An intermediate range of middle-quality firms[θL, θH ] around θ∗ never become active exporters. Those with θL < θ < θ∗
have negative expected profits at all periods, while those with θ∗ < θ < θHwould be profitable in the long run once enough buyers have gathered infor-mation about their type. However, for the latter, the present value of theirprofit stream is negative: losses incurred in the initial periods in order to es-tablish a reputation are not made up for with later expected profits. Hencethis range of firms is kept out of export markets by the information asym-metry and the cost of revealing quality. Finally, high-quality firms (aboveθH) are not profitable in the first period but nevertheless choose to entergiven that expected profits from sales in later periods, when a larger portionof the price reflects true quality, exceed initial losses. The negative profitsin their first export periods can be interpreted as investments in building afirm-specific brand name.
4.2.2. Average Quality
The number M (θ, s) of active firms of quality θ having already exporteds times is derived from Proposition 1 and equations (7) and (8).
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High-quality equilibrium. In a HQE, the number M (θ, s) of active firms ofquality θ having already exported s times is:
M (θ, s) =
δsg (θ) if θ < θ∗ and s < T (θ)
0 if θ < θ∗ and s ≥ T (θ)
δsg (θ) if θ ≥ θ∗
(9)
so that the total number N (θ) of active firms of quality θ is 1−δT (θ)
1−δ g (θ) if
θ < θ∗, and 11−δg (θ) if θ ≥ θ∗. The steady-state average quality of exports
in a HQE as a function of µ and exogenous parameters is given by equation(6) as:
θ (µ) = µ0
1−∞∑
T=0
δT+1
[
(
θmθT
)α−1−
(
θmθT+1
)α−1]
1−∞∑
T=0
δT+1[(
θmθT+1
)α−
(
θmθT+1
)α]
(10)
where θ0 ≡ θm. The average quality of active firms is higher than the meanof the unconditional distribution of θ, as lower-quality firms exit earlier thanhigher-quality firms. However, it lies below the perfect information averagequality.
Low-quality equilibrium. In a LQE, the number of active firms of quality θhaving already exported s times is given by:
M (θ, s) =
g (θ) if θ < θL and s = 0
0 if θ < θL and s ≥ 1 or if θL ≤ θ ≤ θH
δsg (θ) if θ > θH
(11)
so that the total number N (θ) of active firms of quality θ is g (θ) if θ < θLand 1
1−δg (θ) if θ > θH . The steady-state average quality of exports in aLQE as a function of µ and exogenous parameters is given by equation (6):
θ (µ) = µ0
1−(
θmθL
)α−1+ 1
1−δ
(
θmθH
)α−1
1−(
θmθL
)α+ 1
1−δ
(
θmθH
)α
(12)
4.2.3. Existence Conditions
A steady-state equilibrium is a fixed point of θ (µ) defined by equation(12) on [θm, θ∗] and by equation (10) on [θ∗,∞). An equilibrium such that
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µ = θ (µ) < θ∗ is a LQE. An equilibrium such that µ = θ (µ) > θ∗ is a HQE.Proposition 2 establishes existence conditions.
Proposition 2 (Existence Conditions).
1. There is always at least one steady-state equilibrium.
2. There is one HQE (and zero or a positive number of LQEs) if andonly if θ (θ∗) > θ∗, i.e. if and only if:
α
(
θmθ∗
)
+δ
1− δ
(
θmθ∗
)α
> α− 1 (13)
3. There is no HQE and at least one LQE if and only if θ (θ∗) < θ∗.
Proof: see Appendix A.2.
Hence, depending on the parameters, the rational expectations steady-state falls into one of two regimes: a LQE or a HQE. The number of equi-libria is odd except in the knife-edge case where θ (µ) is tangent to the45-degree line. The type of equilibrium depends on whether the (not neces-sarily unique) fixed point of θ (µ) falls left or right of θ∗. Figure 3 provides agraphical illustration. The figure represents the steady-state average qual-ity of exports θ (µ) as a function of µ (red line). The black diagonal is a45-degree line, and we plot a vertical dotted line at the perfect informationthreshold θ∗. The upper left figure 3a illustrates the existence of a HQE:θ (θ∗) > θ∗ and there is one HQE, µ′
S . This equilibrium is not unique: thereare also two LQEs, µS and µU . In the upper right figure 3b, there is also aHQE but it is the unique equilibrium of the economy. On the contrary, thebottom left figure 3c illustrates the fact that when θ (θ∗) < θ∗, there is noHQE. In this example, there is a unique LQE, µS . Finally, the bottom rightfigure 3d illustrates the case with several LQEs and no HQE.
The existence condition (13) for a HQE holds for δ (the probabilitythat a firm still exists from one period to the next) high enough, α (theshape parameter of the distribution) low enough, and k (the costs thatare independent of quality) and w (the costs that increase with quality)low enough. Figure 4 depicts this existence condition. In the dark region,condition (13) holds and there exists one HQE. In subfigure 4a, we fix thevalues of k and w and show that there exists a HQE if α is low enough and δ ishigh enough. A high δ implies that exogenous exit is relatively less prevalentthan endogenous exit, increasing the relative mass of high-quality firms. Alow α means that there is high dispersion in the prior distribution of θ and
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(a) Multiple LQEs and one HQE (b) No LQE and a unique HQE
(c) No HQE and a unique LQE (d) No HQE and multiple LQEs
Notes: In subfigure 3a, the fixed parameter values are: θm = 1, α = 2.2, δ = 0.7, k = 1.2,w = 0.5. The perfect information threshold is θ∗ = 2.4. The steady states of this economyare µS ≈ 1.900, µU ≈ 2.230 and µ′
S ≈ 2.477. In subfigure 3c, the parameters are the sameexcept α = 2.4. The unique steady state of this economy is µS ≈ 1.767. In subfigure 3b,the fixed parameter values are the same as in subfigure 3c except δ = 0.8. The uniquesteady state of this economy is µS ≈ 2.492. In subfigure 3d, the fixed parameter valuesare: θm = 1, α = 3, δ = 0.5, k = 1.18, w = 0.3. The perfect information threshold isθ∗ ≈ 1.686, and the steady states are µS ≈ 1.540, µU ≈ 1.660 and µ′
S ≈ 1.678.
Figure 3: Unique and multiple equilibria
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therefore more firms at the right tail of the distribution pushing up the mean.Note that this result is related to Chisik (2015), who develops a model ofstatistical discrimination and productivity signaling with stereotype threat.He finds that the existence of multiple self-fulfilling steoretypes is more likelyif there is less variance in the ability distribution.
In subfigure 4b, we fix the values of k and δ. There exists one HQE if w islow enough. Intuitively, a low w reduces the relative cost advantage of low-quality firms, as well as the loss incurred in initial periods by high-qualityfirms. Similarly, a low k also reduces the initial losses of high-quality firmsand lowers the perfect information threshold θ∗, expanding the existenceregion of a HQE.
(a) (b)
Notes: Fixed parameter values in subfigure 4a: θm = 1, k = 1.5, w = 0.5. Fixedparameter values in subfigure 4b: θm = 1, k = 1.5, δ = 0.95.
Figure 4: Parameter values for the existence of a HQE
4.3. Equilibrium Stability and Reputation Shocks
A steady-state equilibrium is stable if after a small shock to the countryreputation µ, the economy reverts to the initial equilibrium. We characterizethe stability properties of HQEs and LQEs in Proposition 3.
Proposition 3 (Equilibrium stability).
1. A HQE is always stable.
2. A LQE µS is stable if θ(µ)µ is locally decreasing at µS.
3. A LQE µU is unstable if θ(µ)µ is locally increasing at µU .
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Proof: see Appendix A.3.
The intuition of the stability results relies on entry and exit decisions.In a HQE, it follows from (10) that θ (µ) is continuously decreasing in µon [θ∗,∞). Improving national reputation does not affect the incentives offirms above θ∗ to stay or exit, but it encourages lower-quality firms to staylonger. Hence, starting from a HQE, an improvement in national reputationµ has a negative effect on actual quality, which ensures that a high-qualitysteady state is stable.
In a LQE, θ (µ) as derived in (12) is not necessarily monotonic over[θm, θ∗]. On the one hand, a higher µ reduces the initial loss incurred byhigh-quality firms, allowing more firms with above-average quality to beactive. On the other hand, a better reputation enables more firms to realizepositive profits from first-period sales; this fosters entry by firms with below-average quality. The net change in the average quality depends on thebalance between these two effects. If θ (µ) /µ is locally decreasing in µ (i.e.θ crosses the 45-degree line from above), the former dominates and the LQEis stable. If θ (µ) /µ is locally increasing in µ (i.e. θ crosses the 45-degreeline from below), the latter dominates and the LQE is unstable.
The equilibrium structure implies that in the presence of multiple equi-libria, pure reputation shocks can have long-run effects even without anyindependent change in fundamentals.15 Starting from a stable equilibrium,suppose there is a negative reputation shock, i.e. a one-shot decrease in µt
absent any change in the underlying quality distribution of firms. If theeconomy has only one long-run equilibrium, it must return to this steadystate in the long run. If the economy has multiple steady states, however,reputation shocks can induce a transition to a different equilibrium. A smallreputation shock only has short-lived effects as the economy reverts to its ini-tial equilibrium, but a large enough reputation shock can have self-fulfillingeffects. Figure 3a above provides an illustration of this case when three equi-libria exist. If the initial stable equilibrium is the HQE µ′
S , a “large”shockµt below the unstable LQE µU deteriorates national reputation both in theshort- and in the long-run. The new steady-state equilibrium is the LQEµS .
Hence, our model predicts that there can be long-term consequences ofa sudden large drop in reputation, which moves a country to a less desir-
15Negative reputation shocks have been analyzed empirically through event studies, suchas recalls of Chinese toys (Freedman et al., 2012) or the negative perception of France inthe US at the onset of the Iraq war (Michaels and Zhi, 2010).
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able steady-state equilibrium. In particular, large product recalls or heavilymediatized consumer safety scandals concerning exports of one country canpermanently affect the structure of its industry, lowering both quality andreputation in the long-run.
5. Policy Implications
How can countries improve their “national brand name”– and is it worthit? First-best policies would involve conducting verifiable quality audits ortaxing low-quality firms and subsidizing high-quality ones. These policiesare not feasible when policy-makers are not better informed than consumersabout firms’ quality levels. We analyze the effects of three policy instrumentson reputation, quality and welfare: (i) export subsidies, (ii) a tax schemebased on export tenure, and (iii) minimum quality standards.
5.1. Export Subsidies
Export subsidies have been used historically by a number of countries tofavor exporting activities. For example in South Korea, public investmentsubsidies were tied to exporting activity in the 1970s, as Korean governmentswere determined to favor the emergence of the country on the internationaltrade scene.16 In our model an export subsidy is a permanent17 unantici-pated subsidy to fixed export costs, resulting in a lower effective k for activeexporters, financed by non-distortionary lump-sum taxes.
Interestingly, export subsidies have opposite effects in the two types ofequilibria. In a LQE, an export subsidy leads to higher entry by firms inthe middle of the quality distribution. We show that the overall effect onaverage quality, and thus steady-state national reputation, is positive aslong as δ is not too low: starting from a LQE, an export subsidy increaseslong-run equilibrium quality and the welfare of the exporting country.18 Onthe contrary, in a HQE, an export subsidy is actually detrimental to welfareas it discourages exit by low-quality firms, worsening the problem of sociallyexcessive entry. These results are summarized in Proposition 4.
16Pack and Westphal (1986), Westphal (1990), Levy (1991), Rodrik (1995) and Aw et al.(1998) have documented the importance of government investment subsidies in Korea.
17We are comparing the long-run industry equilibria with and without the policy. Witha subsidy of limited duration, if the equilibrium is unique, the economy would return tothe initial steady state in the long-run after the subsidy expires.
18Since there are no domestic consumers in our model and foreign consumers alwaysreceive a zero surplus, the welfare of the exporting country is composed of exporters’profits and fiscal balance.
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Proposition 4 (Export Subsidy).
1. An export subsidy in a LQE increases the steady-state average qualityof exports and welfare of the exporting country.
2. An export subsidy in a HQE decreases the steady-state average qualityof exports and welfare of the exporting country.
Proof: see Appendix A.4.
More specifically, in a LQE, a decrease in k induces more relatively high-quality firms to start and continue exporting (lower θH) and more relativelylow-quality firms to export for one period (higher θL). The net effect ofthis entry response is an increase in average quality, which creates a positiveexternality on firms that would be exporting regardless of the policy. Theyreceive higher prices on their exports due to improved reputation. Newexporters also benefit from the better reputation as well as the subsidy, sothat the increase in aggregate profits exceeds the tax cost of the subsidy.19
The welfare gain is a direct outcome of higher long-run reputation.20
In a HQE, however, a permanent export subsidy lowers average qualityby inducing low-quality firms to remain exporters longer, while it does notchange the incentives and decisions of high-quality firms. The number ofactive low-quality firms increases but the number of active high-quality firmsremains unchanged. The lower average quality in turn damages the country’sreputation, which decreases the profits of all exporters. Because of thisnegative externality from excessive entry, the overall increase in aggregateprofits of all firms receiving the subsidy is not large enough to cover the costof the policy, despite a higher volume of sales.21
Overall, the desirability of an export subsidy depends on the trade-offbetween encouraging entry by high-quality firms which are deterred by the
19In a setting where firms would set prices in a competitive way, we would have tobalance this gain against the argument that an export subsidy tends to subsidize foreignconsumers.
20Figures A.1 and A.2 in the online Appendix provide a numerical examples of thetransition paths to the new steady states starting from, respectively, a LQE and a HQE.
21We can decompose the welfare effect into two components. For the combination ofquality and export experience for which firms are active both with and without the subsidy,the effect is negative: they receive lower prices and the additional profits brought aboutby the subsidy are taken out of taxes. For the additional periods in which firms below θ∗
stay in the market because of the subsidy, their profits fall short of the cost of the subsidy:otherwise, since the price is lower than in the absence of the policy, they would havebeen exporting without the subsidy. Therefore, the total welfare change is unambiguouslynegative.
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Notes: The initial parameter values are identical to subfigure 3a. The export subsidy isa reduction in k from 1.2 to 1.15. The initial θ∗ is 2.4 and the post-policy θ∗ is 2.3.
Figure 5: Equilibria before and after an export subsidy
cost of establishing a reputation, and inducing entry by low-quality fly-by-night firms. The former impact dominates for countries initially exportinglow-quality goods, while the latter prevails for countries that already ex-port a large share of high-quality goods. Figure 5 illustrates how an exportsubsidy shifts the average quality function and affects the steady state equi-libria. In this example, starting from a situation with two LQEs and oneHQE, the export subsidy eliminates all but one equilibrium which is a HQE.The post-policy unique steady state is higher than the pre-policy LQEs butlower than the pre-policy HQE.
The distinction between the two regimes is new compared to the existingliterature. It reconciles the argument that export subsidies can help high-quality firms enter a market when they are initially unable to separate fromlow-quality firms (as in Bagwell and Staiger, 1989) with the criticism byGrossman and Horn (1988) according to which the marginal entrants arethose with the greatest incentive to produce low-quality goods. Our modeldelivers both of these predictions, depending on the initial equilibrium type.It suggests, in particular, that the gain from such policies – or lack thereof –may critically depend on the level of development and export sophisticationof the exporting country.
5.2. A Tax and Subsidy Program
Let us now assume that the government is able to observe the “age”of a firm, i.e. the number of periods it has previously exported. Start-ing from a LQE, is there a tax/subsidy scheme based on the duration ofexport experience that replicates the perfect information outcome? It is
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noteworthy to observe first that a temporary subsidy (subsidizing entrants)can never do better than a permanent subsidy to all exporters. A subsidythat targets new firms only disproportionately benefits low-quality firms,which account for a higher share of entrants than incumbents. As such,infant industry protection in the traditional sense is counterproductive inour model: it would lower average quality, worsen the country’s reputationand hurt overall profits. A more promising alternative is to tax entrants andsubsidize incumbents, so as to improve the relative payoffs of high-qualityfirms compared to low-quality firms. In order to replicate the perfect infor-mation equilibrium, the tax should deter firms below θ∗ from entering themarket, but the subsequent subsidy should be sufficient to enable all firmsabove θ∗ to earn positive intertemporal profits. However, the design of thetax/subsidy scheme must take into account the fact that if it is successful,the endogenous reputation change also affects the profitability of entry andexit. In fact, we show that when using taxes and subsidies based on age toreplicate the perfect information outcome, the policy involves taxing firmsfor a number of periods and only subsidizing the most mature exporters.
Proposition 5 (Taxes and Subsidies based on Export Experience).The perfect information entry and exit decisions by quality and export ex-perience can be replicated by the following tax/subsidy scheme, where τs isthe tax (possibly negative) levied on a firm that has previously exported s−1times:
τ1 =
(
α
α− 1
)
k
1− w− k − wθm > 0
τs =
[
1− ρ (s− 1) +1− δ
δ
]
1
α− 1
k
1− w−
(
1− δ
δ
)
τ1 for s > 1
The resulting steady-state average quality and reputation are(
αα−1
)
θ∗.
Proof: see Appendix A.5.
The tax/subsidy scheme needs to satisfy three conditions. First, the first-period tax needs to be high enough that no firm below θ∗ earns positiveprofits in the first period. This is ensured by setting τ1 at least equal tothe first-period profits of the lowest quality firm. Second, the taxes onincumbents need to be large enough not to induce any firm below θ∗ toenter and stay beyond the first period despite initial losses. Third, thetaxes on incumbents also need to be small enough to allow all high-qualityfirms above θ∗ to realize positive expected profits over time. These three
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conditions are achieved by setting the tax and subsidy rates as in Proposition5. τs is decreasing in s and is negative for large enough s. An importantpoint is that there needs not be a large subsidy for continuing exporters,because the endogenous change in reputation acts as an implicit subsidy forfirms which are still active exporters after the policy is put in place. Bydiscouraging the entry of low-quality firms, the tax on entrants improvesthe country reputation, which allows the remaining firms in the market tocharge higher prices. The price effect makes up partially or fully for theeffect of the tax on profits, in such a way that the government needs tocompensate these firms less through later subsidies.
As long as the government can observe the export tenure of each firmand there is no cost of collecting taxes and distributing subsidies, thistax/subsidy scheme is optimal from a global and domestic welfare point ofview. However, it has a distributional impact as not all firms benefit fromthe policy. On the one hand, the low-quality firms that would export with-out the tax (below the initial θL) lose profits. On the other hand, the firmsthat become exporters because of the policy (initially between θ∗ and θH)gain as they are now able to realize positive profits; and firms that export inboth cases (above θH) gain from higher prices brought about by the bettercountry reputation. Overall, the improvement in reputation raises globalwelfare. Since all the surplus is captured by the home country through thepricing mechanism, the losses incurred by firms pushed out of the market,whose production is socially inefficient, are more than offset by the gains ofthe new and remaining exporters.
The large first-period tax can be interpreted as an export license. Allentrants are required to pay the initial tax, while only high-quality firmsbenefit in equilibrium from the lower tax rates in later periods and eventu-ally from a subsidy. In this regard, the policy resembles the export licenseor quality stamp explored by Chisik (2003) whereby an optional tax is re-bated only to firms that produce high quality. Chisik (2003) finds that thispolicy supports a separating equilibrium and improves welfare, but he needsto assume that the government perfectly observes the quality of a firm’s ex-ported products after the first period. Our tax and subsidy program relaxesthis assumption by only requiring that the government observes the exporttenure of each firm. From this point of view, it is closer to the introductorytax and mature phase subsidy described by Bagwell and Staiger (1989), butwe generalize their result to a large number of periods and types and takeinto account the endogenous response of consumer beliefs.
Our solution has the novel feature that it depends on the variance of thequality distribution. The taxes τ1 and τs are decreasing in the shape pa-
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rameter α (for all s), which implies that they are increasing in the varianceof the distribution of firm quality types. Similarly, the post-policy equilib-rium quality and reputation increase with variance. A higher variance doesnot affect the perfect information threshold but raises the average qualityof firms above the threshold. Therefore, the equilibrium country reputationunder the policy is higher the higher the variance. Low-quality firms wouldstand to make larger pre-tax profits if they were to enter, hence a higherpath of taxes is needed to deter them and to support the perfect informationoutcome.
Lastly, a caveat is that this policy may suffer from a time inconsistencyproblem, a point also raised in Bagwell and Staiger (1989) and Chisik (2003).Once low-quality firms have decided not to enter, the government has no fur-ther incentive to carry through with the announced taxes and subsidies oncontinuing exporters. This concern can be alleviated by the fact that it isa repeated game. In our model with an infinite horizon and new cohortsof firms every period, if new firms can observe the taxes paid and subsidiesreceived by older generations of firms, the announced policies need to be im-plemented for the government to maintain its credibility with new entrantsand sustain the higher steady-state equilibrium. However, such a coopera-tive equilibrium might not be sustainable, for example if government officialsare not re-electable or if there are term limits.
5.3. Minimum Quality Standards
Finally, we examine the effect of imposing minimum quality standards.An advantage of minimum quality standards is that they are not affectedby the time inconsistency problem. Quality standards have been used byJapan, for instance, in the aftermath of World War II. At that time, “Madein Japan” goods had a reputation for being cheap low-quality goods. Toimprove their “national brand”, both Japanese private companies and thegovernment proceeded to impose strict quality norms (Matsushita, 1979).22
Providing product quality assurances to importers stimulated growth in ex-ports, improved terms of trade, and was key to establish a reputation forproduct quality (Lynn and McKeown, 1988).
We model a minimum quality standard (MQS) as a quality thresholdθMQ. We assume that firms of quality lower than θMQ are never able to sell
22Japanese firms formed export cartels which provided product quality guarantees, bysetting product design and quality standards, establishing industry brand names, guaran-teeing delivery schedules and mediating disputes between individual exporters and foreignbuyers (Dyck, 1992).
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their products.23 We focus on the situation in which the economy is initiallyin a LQE.
If there is no cost of implementing the standard, then from a globalwelfare point of view, it is optimal to set θMQ = θ∗. In other words, it issocially inefficient to let firms of quality below θ∗ enter the export market.However, not all firms benefit from the standard. Let us call µinit the initialsteady-state reputation, and define θL,init and θH,init as the correspondingthresholds. Firms with quality θ < θL,init lose from the policy: they weremaking positive profits from a fly-by-night strategy before the introductionof the standard, but are shut out of the market afterwards. The gains fromintroducting a MQS are reaped by firms with quality θ∗ < θ < θH,init, whichwere not exporting in the initial equilibrium, and by firms with qualityθ > θH,init, which were already exporting but receive extra profits broughtabout by a higher reputation (see Appendix A.6 for details).
Suppose now that the cost of implementing the standard is c (θMQ) andis strictly positive for any θMQ > θm. If the implementation cost doesnot depend on the threshold, i.e. if c′ (θMQ) = 0, the welfare-maximizingthreshold conditional on the existence of the policy is still θ∗. However,if the cost of certifying quality is higher than the welfare gain from theresulting improvement in reputation, then it is too costly for the governmentto support the perfect information equilibrium and the optimal policy is toset no standard at all.
The most interesting case is one in which the cost of inspection increaseswith the threshold, i.e. c′ (θMQ) > 0. Then even if c (θ∗) is high enoughthat it is not worth implementing the perfect information outcome, settingthe standard at a lower level can still be welfare-enhancing. While the non-linearity of quality and reputation precludes us from deriving a closed-formsolution for the optimal MQS, we can show that even a small standard cansupport a HQE. Figure 6 illustrates such a case. In this example, a lowMQS is implemented. It results in an upwards shift in the average qualityfunction, which eliminates the LQEs of this economy. Starting from thestable LQE, the economy transitions towards the unique post-policy HQE.It is noteworthy that, first, the standard did not need to be set at a highlevel to induce this transition; and second, such a policy also improves thesteady-state reputation when the economy starts in a HQE, contrary to
23For the sake of simplicity, we assume that the inspection probability is always equalto 100%. A controlled non-compliant firm has to exit the export market after it incursthe production cost wθ + k and before it can sell its good. Controlled firms of qualityθ < θMQ thus make losses, and in equilibrium never enter.
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Notes: The initial parameter values are identical to subfigure 3a. The perfect informationthreshold is θ∗ = 2.4. The minimum quality standard truncates the distribution of activefirms at θMQ = 1.05.
Figure 6: Equilibria before and after the introduction of a low MQS
export subsidies.Lastly, it may be too costly for the government to set a minimum qual-
ity standard high enough to support a HQE. In such cases, if the cost ofcertifying quality is too high and the government is unable to pre-committo a path of future taxes, the best policy may be to supplement the MQSwith export subsidies.
6. Conclusion
We have shown that when consumers are not fully informed about thequality of what they buy, national reputation matters for exporters. The in-ability to reveal quality to consumers before purchase distorts the incentivesto enter export markets for new firms. Low-quality firms rely on the nationalbrand, while high-quality firms suffer from it. More broadly, unobservablequality tilts the long-run quality composition of an export-oriented industrytowards its low end, all the more so as the exporting economy has a poorreputation for quality. In that respect, reputation has self-perpetuating fea-tures since future national reputation adjusts to past exports quality. Theseissues are particularly relevant for developing countries trying to grow intoexporting increasingly sophisticated goods. National reputations create his-tory dependence in the range of goods a country can successfully export.A damaged national reputation is a barrier to entry for companies that de-velop more expensive high-quality products, threatening the success of sucha growth strategy. In those cases, we have examined several possible pol-icy responses designed to enhance the quality reputation and welfare of an
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exporting country.This analysis suggests several avenues for future empirical research. In
our model, the rational expectations steady-state can fall into one of twocategories. In a high-quality equilibrium, all firms are able to export: low-quality firms enter initially as fly-by-nights and eventually exit after a givennumber of periods; high-quality firms enter and keep exporting. In a low-quality equilibrium, an intermediate range of middle-quality firms never be-come active exporters. This difference in the sorting of firms into exportersand non exporters may be useful for future empirical research to identifylow-quality traps. In addition, case studies have already provided evidenceof the benefits of a reputation for quality in terms of brand premia (Imbset al., 2010) and image spillovers across products of the same brand (Sulli-van, 1990). We develop these insights further by considering the demand forimports, where initial priors depend on country-of-origin and reputations arebuilt not only for specific firms but also for exporting countries as a whole.Our findings could lay the ground for future research analyzing empiricallythe extent to which country reputations matter for trade flows.
Going further, our analysis provides a framework for a richer under-standing of firms’ sourcing decisions through the lens of a strategic use of“made in” rules. Exporters can find it optimal to resort to original equip-ment manufacturers or depart from the cost-minimizing way of splitting theproduction process across locations, in order to obtain a favorable country-of-origin denomination. The location of manufacturing and assembly willbe decided not only according to cost considerations, but also depending onthe regulations surrounding rules of origin, consumer sensitivity to quality,and the degree of asymmetric information in the industry. An extension ofour model along these lines would generate testable predictions at the firmlevel. These topics will be investigated in future research.
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Appendix A. Proofs
Appendix A.1. Proof of Proposition 1: Sorting of Firms into Exports
Appendix A.1.1. High-Quality Equilibrium
Assume there is a steady state equilibrium where µ > k1−w . First,
consider firms with θ < θ∗ born at date t. Since their expected profitsare decreasing with time, they are active in the first period if and only ifEtπt+1 (θ) = µ − wθ − k > 0, which requires θ ≤ µ−k
w . Since µ > k1−w ,
it is straightforward that µ−kw > µ > θ∗ which ensures Etπt+1 (θ) > 0 for
all firms born at t which have quality θ < θ∗. Hence all such firms enterinitially. Also, θ < k
1−w and ρ′ > 0 imply that Etπt+s in (4) is decreasingin s and lims→∞Etπt+s = (1− w) θ − k < 0 so all firms below θ∗ expect toexit in finite time when their profits turn negative. The expected number ofperiods a firm θ born at t is active is T (θ) given by [1− ρ (T (θ − 1))]µ >[w − ρ (T (θ)− 1)] θ + k and [1− ρ (T (θ))]µ < [w − ρ (T (θ))] θ + k.
The highest quality type θT that exits after selling for T periods (or thelowest quality type that exits after selling for T + 1 periods) is defined byEtπt+T+1 (θT ) = 0, hence
θT = max
{
k − [1− ρ (T )]µ
ρ (T )− w, θm
}
(A.1)
and θT is increasing with T : ∂θT∂T ∝ ρ′ (T ) (µ (1− w)− k) > 0 as ρ′ >
0 and µ > θ∗
Second, consider firms with θ∗ < θ < µ. These firms expect pos-itive profits at all periods: they have Etπt+s (θ) monotonically decreas-ing, from πt+1 (θ) = µ − wθ − k > µ (1− w) − k > 0 since θ < µ, tolims→∞Etπt+s (θ) = θ (1− w) − k > 0 since θ > θ∗. Hence firms withθ∗ < θ < µ always enter the market and stay until they are exogenouslyforced to exit.
Finally, consider the highest quality firms with θ > µ. Such firmshave increasing expected profits over time. They enter the market if andonly if their expected intertemporal profits are positive, which requires:Et
(∑
∞
s=1 δs−1πt+s (θ)
)
=∑
∞
s=0 δs [(ρ (s)− w) θ + (1− ρ (s))µ] − k
1−δ > 0or equivalently:
θ >k − µ (1− δ)
∑
∞
s=0 δs (1− ρ (s))
(1− δ)∑
∞
s=0 δsρ (s)− w
≡ θH (A.2)
Let us show that θH < µ. Rearranging:θH < µ iff µ [(1− δ)
∑
∞
s=0 δs (1− ρ (s)) + (1− δ)
∑
∞
s=0 δsρ (s)] > wµ+ k
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or equivalently iff µ > k1−w which holds by assumption in the high reputation
case. Hence all firms with θ > µ always export until they are hit by theexogenous shock.
Appendix A.1.2. Low-Quality Equilibrium
Assume there is a steady state equilibrium with µ < k1−w . First, consider
firms with θ < µ born at date t. Since their expected profits are decreasingwith time, they are active in the first period if and only if Etπt+1 (θ) =µ − wθ − k > 0, which requires θ ≤ µ−k
w ≡ θL. We can immediately check
that µ < k1−w ⇔ θL < µ. Expected second-period profits are Etπt+2 (θ) =
(ρ (1)− w) θ+(1− ρ (1))µ−k < (1− w)µ−k < 0 since θ < µ and ρ (1) > w.Hence among firms with θ < µ, those with θ < θL are active in the firstperiod and exit afterwards, and those with θL ≤ θ < µ are never active.
Second, consider firms with µ ≤ θ < θ∗. These firms have Etπt+1 (θ) < 0since θ > θL, Etπt+s (θ) monotonically increasing in s since θ ≥ µ, andlims→∞Etπt+s (θ) < 0 since θ < θ∗. Thus their expected profits are negativein all periods and they optimally exit after drawing their quality parameter.
Third, consider firms with θ > θ∗. These firms have Etπt+s (θ) monoton-ically increasing in s since θ > µ, and lims→∞Etπt+s (θ) > 0 since θ > θ∗.If they decide to be active in the first period, they expect to remain in themarket as long as they survive the exogenous shock. However given θ > θLthey incur a loss in the initial periods. The condition for a firm of typeθ > θ∗ to be active is for intertemporal expected profits to be positive,
which requires θ >k−(1−Aρ)µ
Aρ−w ≡ θH as derived in (A.2), where we define
Aρ ≡ (1− δ)∑
∞
s=0 δsρ (s). Finally, θH > θ∗ iff
k−(1−Aρ)µAρ−w > k
1−w which sim-
plifies to k1−w > µ and holds by definition in the low reputation case. Hence
firms with θ∗ ≤ θ ≤ θH are never active and firms with θ > θH enter theexport market and stay active.
Lastly, the equilibrium reputation must satisfy µ > k + wθm. Supposeµ is a steady state reputation and µ < k + wθm. The first period price µdoes not cover the production cost of the lowest quality firm, hence no firmbelow θ∗ finds it profitable to enter. It follows that no rational expectationsequilibrium can have µ < θ∗, so there is no LQE with µ < k+wθm. Similarly,if θ∗ < µ < k + wθm, then firms with θ < µ would have negative profitsin all periods. Hence such firms are never active, and µ cannot be a HQEreputation under rational expectations.
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Appendix A.2. Proof of Proposition 2: Existence Conditions
Proposition 2 establishes the existence of at least one steady state equi-librium and the possibility of multiple equilibria. We investigate how θ (µ)varies with µ on [θm,∞). Then, we compute the fixed points of the functionθ (µ), and show that there can be multiple fixed points.
Appendix A.2.1. Average Quality Function
Given Proposition 1 and equation (6), the average quality θ of activefirms in a steady state as a function of the country reputation µ is, on[θm, θ∗]:
θ (µ) = µ0
(1− δ)
(
1−(
θmθL
)α−1)
+(
θmθH
)α−1
(1− δ)(
1−(
θmθL
)α)
+(
θmθH
)α
(A.3)
and on [θ∗,∞):
θ (µ) = µ0
1−∑
∞
T=0 δT+1
(
(
θmθT
)α−1−
(
θmθT+1
)α−1)
1−∑
∞
T=0 δT+1
((
θmθT
)α−
(
θmθT+1
)α)
= µ0
1 +∑
∞
T=TδT
(
θmθT
)α−1
1 +∑
∞
T=TδT
(
θmθT
)α
(A.4)
where T is the lowest value of T such that θT > θm in equation (A.1). Atµ = θ∗, θL = θH = θ∗ and θT = θ∗ for all T . It follows that the functionθ (µ) is continuous at θ∗ since both equations above yield:
θ (θ∗) = µ0
(
1− δ + δ(
θmθ∗
)α−1
1− δ + δ(
θmθ∗
)α
)
(A.5)
Appendix A.2.2. Equilibrium Existence
A steady state equilibrium is a fixed point of the function θ (µ) de-fined in Appendix A.2.1. We have already established that the functionis continuous on [θm,∞). Let us show in addition that θ (θm) > θm and
limµ→∞
θ(µ)µ < 1.
If µ = θm, no firm below θ∗ finds it profitable to export, as nationalreputation imposes a first-period loss on all firms. Some firms with high
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enough θ have a positive NPV of future profits and enter. So since θm is thelower bound of the prior quality distribution, θ (θm) > θ∗ > θm.
As µ → ∞, it remains profitable for all firms to stay active, so firms of allqualities continue exporting until hit by the exogenous shock: T (θ) → ∞ for
all θ. Therefore, limµ→∞ θ (µ) = µ0 which is finite, so limµ→∞
θ(µ)µ = 0 < 1.
By the fixed point theorem, we have established that θ (.) has at leastone fixed point on [θm,∞).
Appendix A.2.3. Existence Condition for a High Quality Equilibrium
A HQE is a steady state equilibrium with equilibrium reputation aboveθ∗. Therefore a sufficient condition for the existence of a HQE is θ (θ∗) > θ∗
in (A.5). We then prove that this is also a necessary condition and that ifthere exists at least one HQE, there is only one HQE.
Let us show that θ (µ) is strictly decreasing in µ on [θ∗,∞). We can
rewrite (A.4) as: θ (µ) = µ0
(
1+K(α−1)1+K(α)
)
where K (α) ≡∑
∞
T=TδT
(
θmθT
)α.
It follows that ∂K(α)∂α =
∑
∞
T=TδT ln (θm/θT )
(
θmθT
)α< 0.
Consider a positive change in one of the thresholds, θS , leaving un-changed all other thresholds. Then all else equal, average quality rises:
∂θ
∂θS=
δS
θS
(
θmθS
)α−1 [
α
(
θmθS
)
(1 +K (α− 1))− (α− 1) (1 +K (α))
]
=δS
θS
(
θmθS
)α−1
(1 +K (α))
[
α
(
θmθS
)
θ
µ0− (α− 1)
]
=δS
θS
(
θmθS
)α−1
(1 +K (α)) (α− 1)
[(
θ
θS
)
− 1
]
> 0
where the positive sign derives from θ > θ∗ > θS for all S in a HQE. Anincrease in µ lowers all θT given Assumptions 1 and 2 and differentiating:∂θT∂µ = − 1−ρ(T )
ρ(T )−w < 0. Thus, in a HQE, θ (µ) is a decreasing function:
∂θ
∂µ=
∞∑
T=T
∂θ
∂θT
∂θT∂µ
< 0
We have proved that θ (.) is strictly and continuously decreasing in µ on[θ∗,∞). It follows that θ (.) has at most one fixed point on [θ∗,∞). Henceθ (θ∗) > θ∗ is a necessary and sufficient condition for the existence of a HQE,and if this condition is satisfied, there is only one HQE.
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Lastly, we express the condition for θ (θ∗) > θ∗ as a function of funda-mental parameters. At µ = θ∗, πt (θ) < 0 for all t > 1 and θ < θ∗. Then:
θ (θ∗) =
∫ θ∗
θmθdG(θ)+ 1
1−δ
∫
∞
θ∗θdG(θ)
∫ θ∗
θmdG(θ)+ 1
1−δ
∫
∞
θ∗dG(θ)
= µ0
(
1−δ+δ( θmθ∗ )
α−1
1−δ+δ( θmθ∗ )
α
)
. So θ (θ∗) > θ∗ is
equivalent to µ0
(
1−δ+δ(
θm(1−w)k
)α−1
1−δ+δ(
θm(1−w)k
)α
)
> k1−w , which after substituting for
the value of µ0 and rearranging yields the following condition for the exis-tence of a HQE:
α
(
θm (1− w)
k
)
+δ
1− δ
(
θm (1− w)
k
)α
> α− 1
Conversely, there is no HQE and there is at least one LQE iff:
α
(
θm (1− w)
k
)
+δ
1− δ
(
θm (1− w)
k
)α
< α− 1
Appendix A.2.4. Multiple Equilibria
While there cannot be more than one HQE, we show that the non-monotonicity of θ (.) on [θm, θ∗] creates the possibility of multiple equilibria.A LQE is a fixed point of θ (µ) given by (A.3) on [θm, θ∗]. On this interval,
we can show that the sign of ∂θ(µ)∂µ is indeterminate. Differentiating with
respect to each threshold:
∂θ
∂θL=
µo (α− 1)
1−(
θmθL
)α+ 1
1−δ
(
θmθH
)α
(
1
θL
)(
θmθL
)α−1 [
1−θ
θL
]
< 0
∂θ
∂θH=
11−δµo (α− 1)
1−(
θmθL
)α+ 1
1−δ
(
θmθH
)α
(
1
θH
)(
θmθH
)α−1 [ θ
θH− 1
]
< 0
∂θ
∂µ=
∂θ
∂θL
∂θL∂µ
+∂θ
∂θH
∂θH∂µ
=µo (α− 1)
1−(
θmθL
)α+ 1
1−δ
(
θmθH
)α × ...
... ×[(
θα−1m
θαL
) [
θθL
− 1]
(
1w
)
− 11−δ
(
θα−1m
θαH
) [
1− θθH
] (
1−Aρ
Aρ−w
)]
∂θ
∂µ< 0 iff
1
1− δ
(
1
θH
)α [
1−θ
θH
](
1−Aρ
Aρ − w
)
>
(
1
θL
)α [
θ
θL− 1
](
1
w
)
This condition can be rewritten as: δ > 1−(
θLθH
)α+1 (θH−θ
θ−θL
)(
(1−Aρ)wAρ−w
)
.
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Then note that the bracketed terms are θLθH
=(µ−k)(Aρ−w)w(k−(1−Aρ)µ)
and θH−θ
θ−θL=
k−(1−Aρ)µAρ−w
−θ
θ−µ−kw
= wAρ−w
(
1−Aρ(θ−µ)k−µ+wθ
)
. Therefore θ (µ) decreases in µ when:
δ > 1−
(
µ− k
k − (1−Aρ)µ
)α+1 (Aρ − w
w
)α−1(
1−Aρ
(
θ − µ)
k − µ+ wθ
)
and increases in µ otherwise. The reason why θ (µ) needs not be monotonicover [θm, θ∗] is that µ has opposite effects on θ coming from θL and θH .Which effect dominates depends on the position of µ as well as the shapeparameter α and the survival parameter δ. This non-monotonicity is whatgives rises to the possibility of multiple equilibria.
To sum up, we have shown that if condition (13) holds, there is one HQE(and there may be zero or a positive number of LQEs). If condition (13)does not hold, there is no HQE and there is at least one LQE.
Appendix A.3. Proof of Proposition 3: Equilibrium Stability
Suppose µS is a steady-state LQE such that ∂θ(µ)/µ∂µ < 0 at µS . We will
show that µS is a stable equilibrium for η < 1. Let us define θL,S ≡ µS−kw and
θH,S ≡k−(1−Aρ)µS
Aρ−w . At time t − 1 the economy is in an initial steady-state
where µS = θ (µS) as given by (12).Assume there is a perturbation at time t such that µt = µS + ε, ε > 0
and ε is small. For all µ ∈ (µS , µS + ε), θ (µ) < µ. The entry thresholds att are:
θL,t =µt − k
w=
µS + ε− k
w
θH,t =k − (1− δ)
∑
∞
u=0 (1− ρ (u))µt+u
Aρ − w
where θH,t is determined by the zero intertemporal profits condition
∞∑
u=0
δu [(ρ (u)− w) θH,t + (1− ρ (u))Etµt+u − k]
and the absence of aggregate uncertainty allows us to remove the expecta-tions operator.
Let us conjecture, to be verified, that µS ≤ µt+u+1 < µt+u < µS + ε for
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all u ≥ 1. Then for all u ≥ 1:
θL,S ≤ θL,t+u+1 < θL,t+u < θL,t
θH,S ≥ θH,t+u+1 > θH,t+u > θH,t
The average quality of exports is determined by the θL and θH thresholdsin the periods after the shock in the following manner: for u ≥ 0,
θt+u = µ0
1−(
θmθL,t+u
)α−1+
u∑
l=0
δu−l(
θmθH,t+l
)α−1+
∞∑
l=u+1
δl(
θmθH,S
)α−1
1−(
θmθL,t+u
)α+
u∑
l=0
δu−l(
θmθH,t+l
)α+
∞∑
l=u+1
δl(
θmθH,S
)α
θL,t+u =µt+u − k
w
θH,t+u =k − (1− δ)
∑
∞
l=0 (1− ρ (l))µt+u+l
Aρ − w
At time t, let us define θpermt as the average quality that would prevail if
firms expected the shock to be permanent, i.e. if Etµt+u = µt for all u ≥ 0.We calculate:
θt = µ0
1−(
θmθL,t
)α−1+
(
θmθH,t
)α−1+ δ
1−δ
(
θmθH,S
)α−1
1−(
θmθL,t
)α+
(
θmθH,t
)α+ δ
1−δ
(
θmθH,S
)α
θt < θpermt = µ0
1−(
θmθL,t
)α−1+
(
θmθpermH,t
)α−1
+ δ1−δ
(
θmθH,S
)α−1
1−(
θmθL,t
)α+
(
θmθpermH,t
)α
+ δ1−δ
(
θmθH,S
)α
as θpermH,t =k−(1−Aρ)(µS+ε)
Aρ−w < θH,t from the conjecture µS ≤ µt+u+1 < µt+u <
µS + ε for all u ≥ 1. Also, we know that θpermt < θ (µS + ε) < µt. The first
inequality results from θH,S > θpermH,t . The second inequality comes from
θ (µ) < µ for µ ∈ (µS , µS + ε). Hence θt < µt and therefore µt+1 = µt +η(
θt − µt
)
< µt. Additionally as long as η is not too close to 1, µt+1 > µS .
We can show, similarly, that in all subsequent periods, θt+u < µt+u aslong as µt+u > µS . Thus µt+u+1 < µt+u for all u and the conjecture thatµt+u follows a decreasing path from µS + ε to µS is verified. In case of a
negative shock to µ at time t starting from a steady state where ∂θ(µ)/µ∂µ < 0,
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the proof is identical with opposite signs. It follows that if µS is a steady-
state LQE reputation and ∂θ(µ)/µ∂µ < 0 at µS , then µS is stable.
By the same reasoning, if µU is a steady-state LQE and ∂θ(µ)/µ∂µ > 0 at
µU , then µU is unstable. Suppose there is a negative shock to µ startingfrom µU = θ (µU ). Let us denote by µS the equilibrium of rank immediately
preceding µU . Further define θL,U ≡ µU−kw , θH,U ≡
k−(1−Aρ)µU
Aρ−w , θL,S ≡ µS−kw
and θH,S ≡k−(1−Aρ)µS
Aρ−w . At time t, µt = µU−ε, where ε > 0 and ε small. Weconjecture µS ≤ µt+u+1 < µt+u < µU − ε, which implies θL,S ≤ θL,t+u+1 <θL,t+u < θL,U and θH,S ≥ θH,t+u+1 > θH,t+u > θH,U for all u ≥ 0. Thenθt+u < µt+u and thus µt+u+1 < µt+u for all u ≥ 0 as long as µt+u > µS .It follows that the economy converges to the steady-state equilibrium ofimmediately lower (or higher in the case of a positive shock) rank whereθ (µ) crosses the 45-degree line from above.
Lastly, the stability of a HQE is derived from a similar proof. Supposethat µQ is the initial steady-state HQE. We know from Appendix A.2.4
that ∂θ(µ)/µ∂µ < 0 at µQ. Let us define θT,Q ≡ max
{
k−[1−ρ(T )]µQ
ρ(T )−w , θm
}
for all
T ≥ 1. Assume there is a perturbation at time t such that µt = µQ + ε,where ε > 0 and ε small.
We conjecture that µQ ≤ µt+u+1 < µt+u < µQ + ε. Then at time t+ u,firms having already exported for T periods exit if their quality parameter
is below θT,t+u given by θT,t+u ≡ max{
k−[1−ρ(T )]µt+u
ρ(T )−w , θm
}
for all T ≥ 1.
It follows that θT,Q ≤ θT,t+u+1 < θT,t+u < θT,t for all T and u ≥ 1. As inthe stable LQE case, we can define θ
permt as the average quality that would
prevail at t if the shock was expected to be permanent. It is straightforwardthat θt < θ
permt < θ (µQ + ε) < µt, from which it follows that µt+1 < µt.
The same reasoning applies to show more generally that µt+u+1 < µt+u forall u as long as µt+u > µQ. Therefore µQ is stable.
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Appendix A.4. Proof of Proposition 4: Export Subsidies
Appendix A.4.1. Low-Quality Equilibrium
In a LQE, average quality is given by (A.3). With ∂θ∂θL
and ∂θ∂θH
derivedin Appendix A.2.4, we obtain:
∂θ
∂k=
∂θ
∂θL
∂θL∂k
+∂θ
∂θH
∂θH∂k
=µo (α− 1)
1−(
θmθL
)α+ 1
1−δ
(
θmθH
)α × ...
×
[
11−δ
(
1θH
)(
θmθH
)α−1 (
1− θθH
)(
1Aρ−w
)
−(
1θL
)(
θmθL
)α−1 (θθL
− 1)
(
1w
)
]
∂θ
∂k> 0 iff
1
1− δ
(
1
θH
)α (
1−θ
θH
)(
1
Aρ − w
)
>
(
1
θL
)α (
θ
θL− 1
)(
1
w
)
This condition can be rewritten as δ > 1 −(
θLθH
)α+1 (θH−θ
θ−θL
)(
wAρ−w
)
.
Note that, starting from a steady-state (θ = µ), the bracketed terms are
θLθH
=(µ−k)(Aρ−w)w(k−(1−Aρ)µ)
and θH−θ
θ−θL=
1Aρ−w
(k−(1−w)µ)
1w(k−(1−w)µ)
= wAρ−w .
Therefore θ decreases in k if and only if
δ > 1−
(
µ− k
k − [1−Aρ]µ
)α+1 (Aρ − w
w
)α−1
The RHS is decreasing in µ and α, so this holds for δ not too low, αnot too high and an initial µ not too low. Then starting from a LQE, adecrease in k moves up the θ (µ) function left of the initial µ. The newsteady-state equilibrium quality and reputation are necessarily higher. Ifthe steady-state is unique, the new steady-state has higher µ. If there aremultiple steady-states, ranked by increasing µ, either the new steady-statehas the same rank and higher µ, or the new steady-state has higher rankand higher µ.
The welfare effect of a subsidy σ (σ = −dk) has three components. First,for firms with θ parameters such that they sell both without and with thesubsidy, the policy adds to their profits the amount it costs to the govern-ment, plus the extra profits brought by a higher reputation µ′ > µ. Thetotal effect is unambiguously positive.
Second, for new exporters that enter around θL because of the policy
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(θL < θ < θL′), the net benefit NBL of the subsidy is positive:
NBL =
∫ θL′
θL
(
µ′ − wθ − k + σ)
dG (θ)−
∫ θL′
θL
σg (θ) dθ
=(
µ′ − k)
∫ θL′
θL
g (θ) dθ − w
∫ θL′
θL
θdG (θ)
=
[
(
µ′ − k)
((
θmθL
)α−
(
θmθL′
)α)
− w αα−1θm
(
(
θmθL
)α−1−
(
θmθL′
)α−1)]
= wθm
[(
θL′
θL
(
θmθL
)α−1−
(
θmθL′
)α−1)
− αα−1
(
(
θmθL
)α−1−
(
θmθL′
)α−1)]
> wθmα−1
(
(
θmθL
)α−1−
(
θmθL′
)α−1)
> 0
where we go from the second to the third line using wθL′ = µ′ − k.Third, for new exporters that enter around θH because of the policy
(θH′ < θ < θH), the net benefit NBH of the subsidy is also positive:
NBH =
∫ θH
θH′
(
∞∑
t=0
δt(
ρ (t) θ + (1− ρ (t))µ′ − wθ − k + σ)
)
g (θ) dθ − ...
... 11−δ
∫ θH
θH′
σg (θ) dθ
= 11−δ
∫ θH
θH′
(
(Aρ − w) θ + (1−Aρ)µ′ − k
)
g (θ) dθ
= 11−δ
[
−(
k − (1−Aρ)µ′)
((
θmθH′
)α−
(
θmθH
)α)
+α(Aρ−w)
α−1 θm
(
(
θmθH′
)α−1−
(
θmθH
)α−1)]
= 11−δ (Aρ − w) θm
[(
(
θmθH′
)α−1−
θH′
θH
(
θmθH
)α−1)
− αα−1
(
(
θmθH′
)α−1−
(
θmθH
)α−1)]
> 11−δ (Aρ − w) θm
α−1
(
(
θmθH′
)α−1−
(
θmθH
)α−1)
> 0
So the overall welfare gain is positive.
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Appendix A.4.2. High-Quality Equilibrium
In a HQE, average quality is given by (A.4). Using the derivations inthe proof of Proposition 2, we obtain:
∂θT∂k
=1
ρ (T )− w> 0 for all T > T
∂θ
∂k=
∞∑
T=T
∂θ
∂θT
∂θT∂k
> 0
Hence a subsidy that lowers k shifts down the θ (µ) function. As θ is de-creasing in µ in the HQE region, the new steady-state equilibrium defined byθ (µ) = µ necessarily has lower µ. So average quality and national reputationare higher in the HQE steady-state without subsidies than with subsidies.
Appendix A.5. Proof of Proposition 5: Tax/Subsidy Scheme
In this section, we show that the age-dependent tax/subsidy in Proposi-tion 5 sustains a steady-state equilibrium which replicates the perfect infor-mation entry and exit patterns by quality level. First, all per-period profits,and therefore all entry or exit decisions, depend on µ, which is itself affectedby the policy. If the tax/subsidy scheme induces decisions identical to theperfect information setting, then firms below θ∗ never enter and firms aboveθ∗ always enter and stay. The resulting average quality and steady-statereputation would therefore be: θ (µ) = µ =
∫
∞
θ∗ θdG (θ) = αα−1θ
∗.Second, let us show that with µ = α
α−1θ∗ and taxes and subsidies set as
in Proposition 5, firms below θ∗ choose never to enter. In the first exportperiod, profits are decreasing in θ. To show that no firm below θ∗ canprofitably enter as fly-by-night and exit after one period, it suffices thata firm of quality θm cannot do so. For firm θm, first-period profits are
πt+1 (θm) = µ−k−wθm−τ1 =α
α−1θ∗−k−wθm−
[
αα−1
(
k1−w
)
− k − wθm
]
=
0.Hence no firm can realize strictly positive first period profits. However,
if subsidies are offered in later periods, it could still be the case that somefirms below θ∗ have an incentive to enter and pay the initial tax in orderto benefit from subsidies in later periods. The tax/subsidy combination fors ≥ 2 ensures that this is not the case. The expected per-period profit of acontinuing exporter is, for s ≥ 2:
Etπt+s (θ) = [ρ (s− 1)− w] θ + [1− ρ (s− 1)]α
α− 1θ∗ − k − τs
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Among low-quality firms, this expression is the highest for firms of qual-ity just below θ∗. Then the definition of θ∗ yields:
Etπt+s (θ∗) = θ∗ − k − wθ∗ +
(
1− δ
δ
)(
τ1 −1
α− 1
k
1− w
)
=
(
1− δ
δ
)(
τ1 −1
α− 1θ∗
)
=
(
1− δ
δ
)
(θ∗ − wθm) > 0
Hence if firm θ∗ enters, it incurs a loss in the first period and positiveprofits thereafter. It follows that it never exits voluntarily and its intertem-poral expected profits are:
Et
∞∑
s=1
δs−1πt+s (θ∗) = πt+1 (θ
∗) +∞∑
s=2
δs−1
(
1− δ
δ
)(
τ1 −1
α− 1θ∗
)
=α
α− 1θ∗ − k − wθ∗ − τ1 + τ1 −
1
α− 1θ∗ = θ∗ − k − wθ∗ = 0
Since the after-tax, after-subsidy profits of continuing exporters are in-creasing in θ, it follows that firms below θ∗ realize negative intertemporalprofits regardless of their exit date and never enter.
Third, by the same token, all firms above θ∗ have initially negativeprofits but a positive net present value of their profit stream, and haveno incentive to exit voluntarily. Finally, note that τs can be rewritten as
τs =(
1−ρ(s−1)α−1
)
θ∗ − 1−δδ (θ∗ − k − wθm) where the second term is nega-
tive. τ1 is positive and given Assumption 1, τs is decreasing in s, τ2 may bepositive or negative, and τs negative for s large enough.
Appendix A.6. Minimum Quality Standard
Let us assume a minimum quality standard θQS = θ∗, such that all thefirms with θ < θ∗ choose not to enter the export market. Thanks to thisminimum quality standard, an economy initially in a stable LQE will moveto a HQE. In this HQE, all the firms of quality θ > θ∗ will export. Thenthe average quality of exports across quality levels and cohorts of firms is
θt =∫
∞
θ∗θNt(θ)dθ
∫
∞
θ∗Nt(θ)dθ
, where the total number of active firms of quality θ is given
by Nt (θ) =1
1−δg (θ). Simple calculations give us θ (µ) = αα−1θ
∗.Let us call µinit the initial steady-state reputation µ (before the minimum
quality standard), and define θL,init ≡µinit−k
w and θH,S ≡k−(1−Aρ)µinit
Aρ−w . Thewelfare effect of the minimum quality standard for the exporting countryhas three components. First, for firms with quality θ < θL,init, the effect is
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unambiguously negative: these firms were exporting as fly-by-night beforethe introduction of the minimum standard making positive profits. Withthe minimum quality standard, they cannot enter the export market. Inthe initial LQE, the total number of active firms of quality θ < θL,init wasg (θ) and given that these firms exported just for one period, their profit wasµinit −wθ − k. Hence the lost profits due to the minimum quality standardare given by:
Loss θ<θL,init=
∫ θL,init
θm
(µinit − wθ − k) dG (θ)
= (µinit − k)
∫ θL
θm
g (θ) dθ − w
∫ θL,init
θm
θdG (θ)
= (µinit − k)
(
1−
(
θmθL,init
)α)
− wα
α− 1θm
(
1−
(
θmθL,init
)α−1)
= wθm
[
θL,initθm
−α
α− 1+
1
α− 1
(
θmθL,init
)α−1]
Second, for firms with quality θ∗ < θ < θH,init, the effect is unambigu-ously positive: these firms were not exporting before the introduction of theminimum standard. With the minimum quality standard, they now enterthe export market and export and stay until they are hit by the exit shock.The value of their profit stream is positive and the gain is given by:
Gain θ∗<θ<θH,init=
∫ θH,init
θ∗
(
∞∑
t=0
δt(
ρ (t) θ + (1− ρ (t))(
αα−1θ
∗
)
− wθ − k)
)
g (θ) dθ
= 11−δ
∫ θH,init
θ∗
(
(Aρ − w) θ + (1−Aρ)(
αα−1θ
∗
)
− k)
g (θ) dθ
= 11−δ
[
−(
k − (1−Aρ)α
α−1θ∗
)(
(
θmθ∗
)α−
(
θmθH,init
)α)
+α(Aρ−w)
α−1 θm
(
(
θmθ∗
)α−1−
(
θmθH,init
)α−1)]
= θm(1−δ)(α−1)
[
(1− w)(
θmθ∗
)α−1− α
θH,init
(
kα + (1−Aρ) (θ
∗ − µinit))
(
θmθH,init
)α−1]
= 1(1−δ)(α−1)
[
k(
θmθ∗
)α− (k + α (1−Aρ) (θ
∗ − µinit))(
θmθH,init
)α]
Third, for firms with quality θ > θH,init, the effect is also unambiguouslypositive: these firms receive extra profits brought by a higher reputation(from µinit to
αα−1θ
∗). For a given reputation µ, the aggregate profit of firms
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with quality θ > θH is given by:
∫
∞
θH
(
∞∑
t=0
δt (ρ (t) θ + (1− ρ (t))µ− wθ − k)
)
g (θ) dθ
= 11−δ
∫
∞
θH
((Aρ − w) θ + (1−Aρ)µ− k) g (θ) dθ
= 11−δ
[
− (k − (1−Aρ)µ)(
θmθH
)α+
α(Aρ−w)α−1 θm
(
θmθH
)α−1]
= 11−δ
[
−k + (1−Aρ)µ+α(Aρ−w)
α−1 θH
] (
θmθH
)α
Hence the gain from the higher reputation is given by:
Gain θ>θH,init=
(
αα−1θ
∗ − µinit
)
(1−Aρ)(
θmθH,init
)α
Overall, the total welfare effect of a minimum quality standard is:
(
αα−1θ
∗ − µinit
)
(1−Aρ)(
θmθH,init
)α
+ 1(1−δ)(α−1)
[
k(
θmθ∗
)α− (k + α (1−Aρ) (θ
∗ − µinit))(
θmθH,init
)α]
− wθm
[
θL,initθm
−α
α− 1+
1
α− 1
(
θmθL,init
)α−1]
From simple computations (derivatives of the lost profits terms Loss θ<θL,init
with respect to various parameters), we obtain that the lower α (the shapeparameter of the distribution), the lower the loss from the minimum qualitystandard. Intuitively, a low α means that there are more firms at the righttail of the distribution, and so relatively less firms that lose from the stan-dard. The lost profits due to the minimum quality standard also decreasewith the costs (w and k) (remember that θLinit =
µinit−kw ). On the contrary,
they increase with the initial reputation (before the standard); the higherthe reputation, the higher the profits the fly-by-night firms were able toextract when they exported for one period.
Appendix B. Informed and Uninformed Buyers
Suppose the population of importers is divided intoN equal-sized groups.There is perfect information diffusion within groups but no information dif-fusion across groups. Thus, if any individual in group n has previously
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consumed the output of firm j, then all buyers in group n are informedabout good j. When firm j is matched with buyer i, i is informed if thereexists iprime ∈ n such that i′ has been matched with j in the past, andi ∈ Uninformed if there is no i′ ∈ n such that i′ has been matched with j inthe past. Further assume that the firm observes in any period whether itsbuyer is informed or not, but not which group the buyer belongs to; henceit does not know the exact proportion of informed buyers in any period butonly its expectation.
It follows immediately from this setup that ρ (0) = 0. After the firmhas exported for one period, one group is informed, so ρ (1) = 1
N . For eachsubsequent period, if the fraction of informed buyers after s export periodsis ρ (s), then with probability ρ (s), the firm is matched with a buyer in aninformed group, and the proportion of informed importers stays at ρ (s) forthe next period. With probability 1−ρ (s), the firm is matched with a buyerin an uniformed group; then the fraction of informed importers next periodis ρ (s) + 1
N .Therefore, the expected fraction of informed buyers is given by the fol-
lowing path: for s ≥ 0,
ρ (0) = 0
ρ (s+ 1) = ρ (s)2 + (1− ρ (s))
(
ρ (s) +1
N
)
= ρ (s)
(
N − 1
N
)
+1
N
We can check that this function satisfies Assumption 1.
ρ (s+ 1)− ρ (s) =1
N(1− ρ (s)) > 0
ρ (s+ 1)− ρ (s)
ρ (s)=
1
N
(
1
ρ (s)− 1
)
is decreasing in s
lims→∞
ρ (s) =1
N
(
1−N − 1
N
)
−1
= 1
So ρ (s) is increasing in s, rises with s at a falling rate, and converges to 1.
Appendix C. Path of Prices for a Given Cohort of Firms
In this Appendix, we characterize the path of prices for a given cohort offirms. At the firm level, there is a “brand premium” for high-quality firmsboth in a HQE and in a LQE: the price charged increases over time fora given good provided that its quality is higher than the country average.
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Result 1 establishes that on average, incumbents receive higher prices thanentrants, and the average price among a cohort of firms is higher, the longerthe cohort has been active on export markets. This result follows from thefact that over time, an increasing fraction of prices reflect firms’ true qualityparameters, and the average quality of a cohort of firms weakly increasesover time as the lowest quality firms exit.
Result 1 (Unit Prices).In a steady-state low-quality equilibrium, the average unit price charged
at t+ s by firms born at date t is strictly increasing in s.In a steady-state high-quality equilibrium, the average unit price charged
at t+s by firms born at date t is strictly increasing in s for all s if µ > αα−1θ1
and for s ≥ T(
α−1α µ
)
otherwise.
Proof. In a LQE, the set of continuing firms is [θH ,∞) from the second
period onwards, so the average price plqet,t+s of cohort t at time t+ s is:
plqet,t+s
(
θ)
=
{
θ if s = 1
θ + ρ (s)(
αα−1θH − θ
)
if s > 1
As θ < θH in a LQE and ρ (s) increases in s, it immediately follows that
plqet,t+s increases with s.In a HQE, the set of active firms of cohort t at time t + s is [θs−1,∞),
and their average price is:
phqet,t+s
(
θ)
=
{
θ if s = 1
θ + ρ (s)(
αα−1θs−1 − θ
)
if s > 1
ρ (s) and θs−1 increase with s. Immediately following the entry of cohort t,
phqet,t+s may fall with s if the distribution of θ has low variance (α high), suchthat α
α−1θ1 > µ. In this case, there is initially a large mass of firms at thebottom of the distribution of continuing firms and their prices are falling.However, since µ < α
α−1θ∗, there is some finite s′ such that for all s ≥ s′,
phqet,t+s+1
(
θ)
> phqet,t+s
(
θ)
and thus at each given point in time, the averageunit price is higher for older cohorts of firms.
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Acknowledgements
We are very grateful to Pol Antras, Elhanan Helpman and Marc Melitzfor their advice. We also thank Philippe Aghion, Philippe Askenazy, DavidAtkin, Eve Caroli, Lorenzo Casaburi, Daniel Cohen, Richard Cooper, Em-manuel Farhi, Shinju Fujihira, David Hemous, Thomas Piketty, MichaelSinkinson, Jean Tirole, Ekaterina Zhuravskaya, and seminar participants atHarvard University, the Paris School of Economics, University of Paris 1and the European Economic Association for helpful comments and sugges-tions. The opinions expressed and arguments employed herein are those ofthe authors and do not reflect the official views of the OECD. Any errorsremain our own.
An online Appendix with additional figures is available at:http://scholar.harvard.edu/cage/publications.
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Under asymmetric information about quality, country reputation affects demand for imported goods.
We obtain two types of steady states: high-quality and low-quality equilibria.
With endogenous reputations, countries may be stuck in low-quality traps (e.g. China).
Export subsidies improve welfare in countries with bad reputation, and decrease it otherwise.
There is a tax/subsidy path based on export experience that replicates the perfect information outcome.